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1. Let D={0,1,2,3,4,5,6,7,8,9} be the set of digits. Let P(D) be the power set of D,...

1. Let D={0,1,2,3,4,5,6,7,8,9} be the set of digits. Let P(D) be the power set of D, i.e. the set of all subsets of D.
   a) How many elements are there in P(D)? Prove it!
   b) Which number is greater: the number of different subsets of D which contain the digit 7 or the number of different subsets of D which do not contain the digit 7? Explain why!
   c) Which number is greater: the number of different subsets of D which contain more than five digits from D (like {0,1,2,5,7,9} or D itself) or the number of different subsets of D which contain less than five digits from D (like {3,4,6,8} or ∅)? Explain why!

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